A dimensionally continued Poisson summation formula

We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When combined with one of the proofs of the Jacobi imaginary transformation of theta functions that does not use the Poisson summation formula, our proof of this generalized Poisson summation formula also provides a new proof of the standard Poisson summation formula for dimensions greater than 2 (with appropriate hypotheses on the function being summed). In general, our methods work to establish the (Voronoi) summation formulae associated with functions satisfying (modular) transformations of the Jacobi imaginary type by means of a density argument (as opposed to the usual Mellin transform approach). In particular, we construct a family of generalized theta series from Jacobi theta functions from which these summation formulae can be obtained. This family contains several families of modular forms, but is significantly more general than any of them. Our result also relaxes several of the hypotheses in the standard statements of these summation formulae. The density result we prove for Gaussians in the Schwartz space may be of independent interest.Comment: 12 pages, version accepted by JFAA, with various additions and improvement

On the Construction of Quantum Field Theories with Factorizing S-Matrices

The subject of this thesis is a novel construction method for interacting relativistic quantum field theories on two-dimensional Minkowski space. The input in this construction is not a classical Lagrangian, but rather a prescribed factorizing S-matrix, i.e. the inverse scattering problem for such quantum field theories is studied. For a large class of factorizing S-matrices, certain associated quantum fields, which are localized in wedge-shaped regions of Minkowski space, are constructed explicitely. With the help of these fields, the local observable content of the corresponding model is defined and analyzed by employing methods from the algebraic framework of quantum field theory. The abstract problem in this analysis amounts to the question under which conditions an algebra of wedge-localized observables can be used to generate a net of local observable algebras with the right physical properties. The answer given here uses the so-called modular nuclearity condition, which is shown to imply the existence of local observables and the Reeh-Schlieder property. In the analysis of the concrete models, this condition is proven for a large family of S-matrices, including the scattering operators of the Sinh-Gordon model and the scaling Ising model as special examples. The so constructed models are then investigated with respect to their scattering properties. They are shown to solve the inverse scattering problem for the considered S-matrices, and a proof of asymptotic completeness is given.Comment: PhD thesis, Goettingen university, 2006 (advisor: D. Buchholz) 153 pages, 10 figure

Phosphorothioate antisense oligonucleotides induce the formation of nuclear bodies

Antisense oligonucleotides are powerful tools for the in vivo regulation of gene expression. We have characterized the intracellular distribution of fluorescently tagged phosphorothioate oligodeoxynucleotides (PS-ONs) at high resolution under conditions in which PS-ONs have the potential to display antisense activity. Under these conditions PS-ONs predominantly localized to the cell nucleus where they accumulated in 20-30 bright spherical foci designated phosphorothioate bodies (PS bodies), which were set against a diffuse nucleoplasmic population excluding nucleoli. PS bodies are nuclear structures that formed in cells after PS-ON delivery by transfection agents or microinjection but were observed irrespectively of antisense activity or sequence. Ultrastructurally, PS bodies corresponded to electron-dense structures of 150-300 nm diameter and resembled nuclear bodies that were found with lower frequency in cells lacking PS-ONs. The environment of a living cell was required for the de novo formation of PS bodies, which occurred within minutes after the introduction of PS-ONs. PS bodies were stable entities that underwent noticeable reorganization only during mitosis. Upon exit from mitosis, PS bodies were assembled de novo from diffuse PS-ON pools in the daughter nuclei. In situ fractionation demonstrated an association of PS-ONs with the nuclear matrix. Taken together, our data provide evidence for the formation of a nuclear body in cells after introduction of phosphorothioate oligodeoxynucleotides

Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics

We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) ows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several special applications in heliophysics and astrophysics, assessing triumphs, challenges,and future directions

Crowd-sourced machine learning prediction of long COVID using data from the National COVID Cohort Collaborative

Background: While many patients seem to recover from SARS-CoV-2 infections, many patients report experiencing SARS-CoV-2 symptoms for weeks or months after their acute COVID-19 ends, even developing new symptoms weeks after infection. These long-term effects are called post-acute sequelae of SARS-CoV-2 (PASC) or, more commonly, Long COVID. The overall prevalence of Long COVID is currently unknown, and tools are needed to help identify patients at risk for developing long COVID. Methods: A working group of the Rapid Acceleration of Diagnostics-radical (RADx-rad) program, comprised of individuals from various NIH institutes and centers, in collaboration with REsearching COVID to Enhance Recovery (RECOVER) developed and organized the Long COVID Computational Challenge (L3C), a community challenge aimed at incentivizing the broader scientific community to develop interpretable and accurate methods for identifying patients at risk of developing Long COVID. From August 2022 to December 2022, participants developed Long COVID risk prediction algorithms using the National COVID Cohort Collaborative (N3C) data enclave, a harmonized data repository from over 75 healthcare institutions from across the United States (U.S.). Findings: Over the course of the challenge, 74 teams designed and built 35 Long COVID prediction models using the N3C data enclave. The top 10 teams all scored above a 0.80 Area Under the Receiver Operator Curve (AUROC) with the highest scoring model achieving a mean AUROC of 0.895. Included in the top submission was a visualization dashboard that built timelines for each patient, updating the risk of a patient developing Long COVID in response to clinical events. Interpretation: As a result of L3C, federal reviewers identified multiple machine learning models that can be used to identify patients at risk for developing Long COVID. Many of the teams used approaches in their submissions which can be applied to future clinical prediction questions